Predicting Highway Safety for Curves on Two-Lane Rural Highway

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HSM Practitioners Guide for Two-Lane Rural
Highways Workshop

• Predicting Highway Safety for Curves on Two-Lane
  Rural Highway

- Session 4
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Predicting Highway Safety for Curves on Two-Lane
Rural Highways

• Learning Outcomes

• Describe the crash prediction method for Crash
  Performance on Horizontal Curves
• Identify low-cost safety improvements for
  horizontal curves

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.Curves present particular safety problems to
designers
CRASH RATES (Crashes per 1 km segment--3 year
timeframe)

• The risk of a reported crash is about three
  times greater on a curve than on a tangent

Crash Rate
Source Glennon, et al, 1985 study for FHWA
Tangent segments
Segments w/curve
Curved portion only (Curve plus transitions)
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Actual Driver Operations on Curves
Driver tracks a critical radius sharper than
that of the curve just past the PC

• Drivers overshoot the curve (track a path
  sharper than the radius)
• Path is a spiral
• Path overshoot behavior is independent of speed

Source Bonneson, NCHRP 439 and Glennon et al
(FHWA)
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Driver overshoot behavior on curves (from
Glennon, et al)
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Example -- a 1000-ft radius curve is driven by a
95th percentile driver at about a 700 ft
radius at some point in the curve
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Research confirms differences in actual
operations versus AASHTO assumptions

• Drivers selected speed behavior does not match
  design assumptions
• Sharper curves (lt80 km/h or 50 mph) are driven
  faster (drivers are more comfortable)

Curves driven faster than Policy assumption
Curves driven slower than Policy assumption
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Speed Prediction Model for Horizontal Curves
(Otteson and Krammes)
V85 41.62 - 1.29D 0.0049L - 0.12DL 0.95 Vt

• Where
• V85 85th percentile speed on the curve
• D degree of curve
• L length of curve (mi)
• Vt 85th percentile approach speed (mph)
• this should be measured in the field

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A risk assessment tool for speed profiles

• V85 - Vdesign Vdelta
• Higher risk curves may be those with V delta
  high (i.e., operating speeds significantly
  greater than design speed)
• Vdelta gt 12 mph (20 km/h) high risk
• 6 mph (10 km/h) lt Vdelta lt 12 mph (20 km/h)
  caution

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FHWAs IHSDM Speed Consistency Model Addresses
Continuous Speed Behavior
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Truck operations on curves may in some cases be
critical (Harwood and Mason)

• Under certain conditions, trucks will roll over
  before they skid
• Trucks with high centers of gravity overturn
  before losing control due to skidding
• Margin of safety for f is therefore lower for
  trucks
• Trucks on downgrade curves generate greater
  lateral friction (superelevation is not as
  effective)

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Summary of Research on Superelevation and
Transition Design

• Studies confirm small but significant effect of
  superelevation on crashes
• FHWA (Zegeer) study noted 5 to 10 greater
  crashes when superelevation is deficient
• 1987 study of fatal crash sites on curves noted
  deficiencies in available superelevation

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Research confirms benefits of spirals and
recommends optimal transition design
Spirals provides e transition leading into the
curve
Radius (m)
Source NCHRP Report 439

• Zegeer et al found safety benefits in HSIS study
  of Washington
• Bonneson confirmed operational benefits noted by
  Glennon, etal

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Zegeer et al. FHWA Study Cost-Effective
Geometric Improvements for Safety Upgrading of
Horizontal Curves (1991)

• Data Bases
• 10,900 Curves in Washington State
• 7-state data base of 5000 mi
• 78 curves in New York State
• Glennon 4-state data base of 3277 curve segments
• Statistical Analysis and Model Development
• Identified as key effort in TRB SR 214, recent
  NCHRP review by BMI, and key reference for IHSDM

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Summary of findings from Zegeer study

• Features related to crashes include
• Degree and length of curve
• Width through the curve
• Superelevation and,
• Spiral presence
• For typical volumes on 2-lane highways, expect 1
  to 3 crashes per 5 years on a curve

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Safety Effects for Horizontal Curves (CMF3r)

• CMF3r 1.55 Lc (80.2/R) - 0.012 S
  1.55Lc
• Where
• Lc Length of Curve including spirals, (mi)
• R Radius of Curve (ft)
• S 1 if spiral transition is present, 0 if not
  present

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Safety Effects of Horizontal Curves (CMF3r)
Example with no Spiral present

• For Lc 480 feet 0.091 miles
• R 350 no spiral transition

CMF3r 1.55 Lc (80.2/R) 0.012S / 1.55Lc
(1.55 x 0.091) (80.2/350)
0.012x0 1.55x 0.091

2.62
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Safety Effects of Horizontal Curves (CMF3r)
Example with Spiral Transition

• For Lc 480 feet 0.091 miles
• R 350 with spiral transition

CMF3r 1.55 Lc (80.2/R) 0.012S / 1.55Lc
(1.55 x 0.091) (80.2/350)
0.012x1 1.55x 0.091
?
2.54
Without spiral CMF3r 2.62, with spiral CMF3r
2.54, Difference 8 potential for fewer
crashes with a spiral transition in this segment.
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Crash Modification Function for Horizontal
Curves Superelevation
CMF4r is based on Superelevation variance or SV

• For SV less than 0.01 CMF4r 1.00
• For 0.01 lt SV lt 0.02 CMF4r 1.00 6(SV-0.01)
• For SV gt 0.02 CMF4r 1.06 3(SV-0.02)

Example Design e 4, Actual e 2
SV 0.04 0.02 0.02
CMF4r 1.06 3(0.02-0.02) 1.06 3(0.0) 1.06
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HSM Applications to Two-Lane Rural Highway
Segments

• HSM Crash Prediction Method for Two-Lane Rural
  Highway Segments
• Applying SPF and CMFs
• Example Problem

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Crash Prediction for Roadway Segment for Existing
Conditions Example Calculation

• Two-Lane Rural Roadway, CR 123 Anywhere, USA (MP
  10.00 15.02)
• AADT 3,500 vpd for the current year
• Length 26,485 feet 5.02 miles
• Lane Width 11.0 ft
• Shoulder Width 2 ft Shoulder Type Gravel
• Horizontal Curve on Grade (MP 12.00-12.186)
• Lc 0.186 miles, R 650 with no spiral
  transition
• Grade 4.5
• Superelevation Variance .02
• Tangent Section on Grade (MP 13.45-14.00)
• L 0.55 miles Grade -6.3

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Crash Prediction for Roadway Segment for Existing
Conditions Example

• Divide Two-Lane Rural Roadway into Individual
  Segments

Segment Length (miles) Horizontal Curve Radius (ft) Super-elevation Variance Grade () Driveway Density (per mile) RHR
10.00 12.00 2.000 Tangent N/A 2.0 8 5
12.00 12.186 0.186 650 .02 4.5 0 5
12.186 -13.45 1.264 Tangent N/A 3.0 4 5
13.45-14.00 0.550 Tangent N/A - 6.3 0 5
1400-15.02 1.020 Tangent N/A - 3.0 6 5
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Safety Performance Function (SPF) for Base
Conditions Example Calculation
Segment 2 (MP 12.00-12.186) Horizontal Curve on
a 4.5 Grade

• Where
• AADT 3,500 vpd (current year)
• Length 0.186 miles

Nspf-rs (AADTn) (L) (365) (10-6) e-0.312
Nspf-rs (3,500) (0.186) (365) (10-6) e-0.312
(3,500) (0.186) (365) (10-6) (0.7320)
0.17 crashes per year
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CMF for Lane Width (CMF1r) Calculation
Segment 2 11 foot wide lane
From Table 10-8 CMFra 1.05

• Adjustment for lane width and shoulder width
  related crashes (Run off Road Head-on
  Sideswipes) to obtain total crashes using default
  value for pra 0.574

CMF1r (CMFra - 1.0) pra 1.0
(1.05 - 1.0) 0.574 1.0
(0.05) (0.574) 1.0
1.03
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CMF or Shoulder Width and Type (CMF2r)
Calculation
Segment 2 2 ft wide gravel shoulder
CMFwra 1.30 (Table10-9) and CMFtra 1.01
(Table10-10)

• Adjustment from crashes related to lane and
  shoulder width (Run off Road Head-on
  Sideswipes) to total crashes using default value
  for pra 0.574

CMF2r (CMFwra CMFtra - 1.0) pra 1.0
((1.30)(1.01) - 1.0) 0.574 1.0
(0.313) (0.574) 1.0
1.18
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CMF for Horizontal Curve (CMF3r) Calculation
Segment 2 Horizontal Curve

• For Lc 0.186 miles
• R 650 with no spiral transition

CMF3r 1.55 Lc (80.2/R) 0.012S / 1.55Lc
(1.55 x 0.186) (80.2/650)
0.012x0 1.55x
0.186
1.43
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CMF for Superelevation on Horizontal Curves
(CMF4r)
Segment 2 Horizontal Curve Superelevation
Variance 0.02

• For SV gt 0.02 CMF4r 1.06 3(SV-0.02)

CMF4r 1.06 3(0.02-0.02) 1.06 3(0.0)
1.06
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CMF for Percent () Grade on Roadway Segments
(CMF5r)
Segment 2 4.5 Grade
CMF5r 1.10
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CMF Roadside Design (CMF10r) Example Calculation

• Segment 2 RHR 5

CMF10r e(-0.6869 (0.0668xRHR)) /e-0.4865
e(-0.6869 (0.0668x5)) /e-0.4865
1.14

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Applying CMFs to the SPF Base Prediction Model
CRASH MODIFCATION FACTORS Lane
Width 11 ft CMF1r 1.03 Shoulder Width 2 ft
gravel CMF2r 1.18 Horizontal Curve CMF3r
1.43 Superelevation Variance (0.02) CMF4r
1.06 Percent Grade 4.5 CMF5r 1.10 Driveway
Density, None CMF6r 1.00 Centerline Rumble,
None CMF7r 1.00 Passing/Climbing Lanes,
None CMF8r 1.00 TWLTLs, None CMF9r
1.00 Roadside Design, RHR 5 CMF10r
1.14 Lighting, None CMF11r 1.00 Automated
Enforcement, None CMF12r 1.00
Segment 2 SPF and CMF Values AADT 3,500
vpd, Length 0.186 mi Radius 650
ft Nspf-rs 0.17 crashes per year CMFtotal 2.31
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Applying CMFs to the SPF Base Prediction Model
Npredicted-rs Nspf-rs x (CMF1r CMF12r) Cr
Segment 2 Apply CMFs to SPF for Base Conditions
(letting Cr 1.0)
0.17 x (1.03 x 1.18 x 1.43 x 1.06 x 1.10 x 1.00 x
1.00 x 1.00 x 1.00 x 1.14 x 1.000 x 1.00) x 1.00
Npredicted-rs
0.17 x 2.31 x 1.00
0.4 crashes per year, 1 crash every 2.5 yrs
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Crash Prediction for Roadway Segment for Existing
Conditions Example Calculation

• For each Two-Lane Rural Roadway Segment Table
  with SPF predicted crahses, CMFs, and Adjusted
  Total Crashes

CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES CRASH PREDICTION METHOD TOTAL CRASHES
Seg No. SPF base CMF1r LW CMF2r SWST CMF3r ST CMF4r e CMF5r Grade CMF6r DD CMF7r CLRS CMF8r PassLn CMF9r TWLTL CMF10r RD CMF11r Light CMF12r Spd Enf Total CMF Total Adjusted Crashes
1 1.87 1.03 1.18 1.00 1.00 1.00 1.07 1.00 1.00 1.00 1.14 1.00 1.00 1.49 2.8
2 0.17 1.03 1.18 1.43 1.06 1.10 1.00 1.00 1.00 1.00 1.14 1.00 1.00 2.31 0.40
3 1.27 1.03 1.18 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.14 1.00 1.00 1.39 1.8
4 0.51 1.03 1.18 1.00 1.00 1.16 1.00 1.00 1.00 1.00 1.14 1.00 1.00 1.61 0.8
5 0.95 1.03 1.18 1.00 1.00 1.00 1.02 1.00 1.00 1.00 1.14 1.00 1.00 1.42 1.4
Total 7.2
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Predicting Crash Frequency Performance
Total Predicted Crash Frequency within the limits
of the roadway being analyzed
Ntotal crashes ?Npredicted-rs ? Npredicted-int
Ntotal crashes 7.2 crashes/yr ? Npredicted-int
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Overview of Good Alignment Design Practice
(suggested by safety and operational research)

• Curves and grades are necessary features of
  alignment design (reflect the topography,
  terrain, and context)
• Pay particular attention to roadside design
  adjacent to curves
• Avoid long, sharp curves
• Adjust alignment design to reflect expected
  speeds on curves

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Overview of Good Alignment Design Practice
(continued)

• Avoid minimum radius designs where
• actual speeds will be higher than design speeds
• truck volumes will be substantial
• combined with steep grades
• Use spiral transition curves, particularly for
  higher speed roads and sharper curves

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Overview of Good Alignment Design Practice
(continued)

• Minimize grades within terrain context
• Widen lanes and shoulders through curves
• Pay attention to access points related to
  horizontal and vertical curve locations

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Low and Lower Cost Safety Improvements for
Horizontal Curves

• Signing

• Shoulders

• Lighting

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Low Cost Intersection Safety Measures Signing
Countermeasures
Advance Warning With Speed Advisory
Injury Crashes CMF 0.87 CRF 13
PDO Crashes CMF 0.71 CRF 29
CMF Clearinghouse http//www.cmfclearinghouse.org
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Safety Effects of Installing Combination
Horizontal Alignment Warning Advisory Speed
Signs
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Signing Countermeasure for Horizontal Curves
Chevrons Signs
CRF 35
CMF 0.65
CMF Clearinghouse http//www.cmfclearinghouse.org
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Safety Effects of Installing RPMs
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Low Cost Intersection Safety Measures Signing
Countermeasures
Double Up Advance Warning Signs
CRF 31 CMF 0.69
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Low Cost Intersection Safety Measures Signing
Countermeasures
Sharp 10 mph curve to right just over hill
Activated Warning Beacon

• Radar activated flasher when speed is fast for
  10mph curve

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Examples of Improving Safety of Existing Curves
Widen Shoulders

• Widen 2 Shoulder to 6 Shoulder NY Rte 82
  north of Millbrook

6
2
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Examples of Improving Safety of Existing Curves
Widen Shoulder on Inside of Tight Curve

• Widening on
• Inside of Curves

NCHRP 500, Strategy 15.2 A11 Widening in Curves
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Low Cost Intersection Safety Measures Signing
Countermeasures

• 9. Illumination of
• Rural Curves

CRF 28 for injury crashes highway lighting
Route 376 near Poughkeepsie, NY
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Predicting Highway Safety for Curves on Two-Lane
Rural Highways

• Learning Outcomes

• Described the equation for prediction of Crash
  Performance on Horizontal Curves
• Identified low-cost safety improvements for
  horizontal curves

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Questions and Discussion